EP1181668B1 - Image coding/decoding method - Google Patents

Description

The field of the invention is that of coding of fixed or moving images. More specifically, the invention relates to image compression techniques, or sequences of images, based on the implementation of transformations reversible mathematics.

Many image compression techniques are known. to reduce the amount of data needed to represent an image or a sequence of moving pictures. We thus seek, in particular, to reduce the flow rates of digital signals, for transmission and / or storage on a data carrier.

The invention applies in particular, but not exclusively. to the transmission of low bit rate image signals, as well as transmissions without guaranteed speed, such as those performed using the IP protocol ("Internet Protocol ”).

Among the many known image coding methods, one can in particular to distinguish the ISO-JPEG and ISO-MPEG techniques, which gave rise to a standard. These coding methods are notably based on the implementation transforms, which allow an efficient elimination of redundancy in a picture.

FIG. 1 illustrates the general principle of a coding method by transformed.

The image to be coded 11 is firstly partitioned into a set of blocks 12 non-overlapping rectangles of the same size, to which a invertible transformation 13. This transformation generates a transformed block 14, formed of a set of transformed coefficients less correlated than the coefficients of the original block 12.

These coefficients then undergo a quantification 15, then a coding 16, before being transmitted (17) on the channel, or stored.

où m ∈[0,M - 1] et n ∈[0,N - 1].If we note I (x, y) the luminance of the pixel of coordinates (x, y) and if we consider that the image to be coded 11 has been partitioned into block 12 of size M x N, the application of a block oriented transformation 13 a (x, y, m, n) will produce an image F with:

where m ∈ [0, M - 1] and n ∈ [0, N - 1].

From the transformation a (x, y, m, n), an inverse transformation b (x, y. M, n) can be defined in order to reconstruct the original image I:

• la transformation de Karhunen Loève (KLT),
• la transformation de Fourier discrète (DFT),
• la transformation en cosinus discrète (DCT),
• et la transformation de Walsh-Hadamard (WHT).

The main transformations used in image compression are:

• the transformation of Karhunen Loève (KLT),
• the discrete Fourier transformation (DFT),
• transformation into discrete cosine (DCT),
• and the Walsh-Hadamard transformation (WHT).

It is important to note that the transformation operation 13, applied alone, does not ensure any compression of the image since its sole purpose is to decorrelate the original data and focus most of energy in a small number of transformed coefficients. Given that the total energy is conserved, most of the transformed coefficients do not contain very little energy, so that's quantization 15 and coding 16 effective of these coefficients which will allow compression.

A good quality transformation must allow a decorrelation efficient, be independent of the images processed, and must have algorithms fast allowing efficient implementation.

The technique that proves to be the most effective for the decorrelation of a signal is the KLT. Unfortunately, it is dependent on the images manipulated (because it is necessary to calculate the signal statistics to deduce the processed). There are therefore no fast algorithms allowing a efficient implementation, which limits its use.

However, for typical images in which there is a strong correlation between the pixels, the performance of the DCT is very close to that of the KLT. In addition, the DCT has many fast algorithms allowing an efficient implementation. In addition, it does not depend on the images manipulated. Finally, it introduces less inter-block deformations than the DFT.

If we consider equation (1), the CSD is obtained by posing: at ( x, y, m, n ) = 2 vs ( m ) vs ( not ) MN cos ( (2 x + 1) π m 2 M ) Cos ( (2 there + 1) π not 2 NOT ) With:

Different compression standards use an approach based on DCT, such as JPEG for still images. H261 and H263 for the sequences video for videophone and videoconference type applications using images in CIF (Common Intermediate Format) and QCIF (Quarter CIF), and finally MPEG (1, 2, and 4), for video sequences of any content, in view digital television applications.

This classic technique however has several limitations, due including the fact that the processing does not take into account the content of the image original. Indeed, the partitioning of the image is based on a division regular and systematic in squares, thus generating block effects, and does not take not sudden transitions between different areas of the image.

Furthermore, the techniques implementing transformations lend themselves trouble with geometric manipulations (zooms, rotations or deformations (warping), ...), which are conventionally used to determine compensation for movement between two consecutive images in the frame animated images (MPEG) or to integrate natural images into synthetic scenes.

The invention particularly aims to overcome these drawbacks of the art prior.

More specifically, an objective of the invention is to provide a method of coding of still or moving images, based on the implementation of a reversible transformation, based on a different partition, based on triangles. he it should be noted that the simple formulation of this objective is part of an approach inventive. Indeed, nowadays, the main transformative approaches suppose a partitioning into square blocks, or a decomposition into regions of any form, but not offering the flexibility of using a partition by mesh.

A particular objective of the invention is to provide such a method, in which the triangular partition is adapted to the semantic content of the image or of the image sequence.

Another object of the invention is, of course, to provide such a method of coding that offers good cost / quality coding (i.e. reconstruction of the image / quantity of data to be transmitted or stored).

The invention also aims to provide such a coding method which is relatively easy to implement, and in particular which does not require a significant number of complex additional operations compared to known techniques.

A complementary objective of the invention is. in one embodiment particular, to provide such a coding method which can be implemented selectively on portions of images, in addition to another approach.

Another object of the invention is to provide a decoding method corresponding, which allows the reconstruction of images in a simple and inexpensive way costly (in processing time, storage capacity, ...).

• définition d'une partition triangulaire minimale, recouvrant ledit domaine ;
• association a chacun desdits triangles source d'une matrice carrée représentative dudit triangle source, à l'aide d'une première transformation réversible ;
• application d'une seconde transformation réversible de décorrélation sur chacune desdites matrices carrées, délivrant des matrices transformées.

These objectives and others which will appear more clearly below are achieved according to the invention using an image coding method, comprising, for a domain corresponding to at least one image portion, the following steps :

• definition of a minimum triangular partition, covering said domain;
• association with each of said source triangles of a square matrix representative of said source triangle, using a first reversible transformation;
• application of a second reversible decorrelation transformation on each of said square matrices, delivering transformed matrices.

Thus, according to the invention, it is possible to apply a technique of reversible transformation on images which are not broken down into squares, but in triangles, the latter can be of any shape (in size and orientation), and different from each other. They can in particular be adapted to image content.

It is thus possible to combine the advantages of techniques based on transformations and techniques implementing a decomposition into triangles, without the extra processing being very important, for compared to the transformations carried out on square blocks.

• transformation affine d'un triangle source en un triangle rectangle isocèle, appelé triangle de référence ;
• création d'une matrice carrée dont la partie inférieure comprend les données représentatives dudit triangle rectangle isocèle ;
• symétrisation de ladite matrice carrée.

Advantageously, said step of associating a square matrix comprises the following steps:

• affine transformation of a source triangle into an isosceles right triangle, called a reference triangle;
• creation of a square matrix, the lower part of which comprises the data representative of said isosceles right triangle;
• symmetrization of said square matrix.

These operations, and the reverse operations, are indeed very simple to enforce.

According to a preferred embodiment of the invention, said matrix square is obtained using bilinear interpolation.

Advantageously, said step of creating a square matrix highlights uses a scale factor α allowing expansion or compression in the space domain. We can easily adapt the number of data necessary to code the image according to needs and / or resources available.

In this case, said square matrix can comprise E (α × 2 × AT ) lines, where E represents the function delivering the upper whole part, A being the area of said isosceles right triangle.

• la transformation de Karhunen Loève (KLT) ;
• la transformation de Fourier discrète (DFT) ;
• la transformation en cosinus discrète (DCT) ;
• la transformation de Walsh-Hadamard (WHT).

Said second transformation may in particular belong to the group of usual transformations in the field, such as for example:

• the transformation of Karhunen Loève (KLT);
• the discrete Fourier transformation (DFT);
• transformation into discrete cosine (DCT);
• the Walsh-Hadamard transformation (WHT).

As we will see later, the DCT currently seems the best adapted.

Preferably, the image coding method according to the invention then includes a step of quantifying and coding the data of the lower part of said transformed matrix. Most of the quantization and coding can be used.

• une quantification uniforme ;
• une quantification à parcours zigzag, le pas de quantification étant incrémenté au fur et à mesure dudit parcours ;
• une quantification basée sur au moins une matrice de pondération pré-évaluée ou optimisée pour l'image traitée.

In particular, said quantification can advantageously belong to the group comprising:

• uniform quantification;
• a quantization with a zigzag course, the quantization step being incremented as and when said course;
• a quantification based on at least one pre-evaluated or optimized weighting matrix for the image processed.

Furthermore, the coding preferably comprises a coding step. RLE ("Run Length Encoding") and entropy quantified data.

Advantageously, the method of the invention is configurable. In particular, it can be provided that said scale factor α, the type of quantification and / or the quantization step can be modified, for each of said triangles and / or for each of said image portions.

The method described applies regardless of the method used to determine the triangles to be treated. According to an advantageous embodiment, said triangular partition is obtained according to a method taking into account the content of the image or portion of the image.

In other words, the vertices and edges of the triangles coincide, as much as possible, with transitions in the image considered.

• les méthodes mettant en oeuvre une DCT ;
• les méthodes à base de décomposition fractale ;
• les méthodes dites "matching pursuit" (ou méthodes de poursuites d'appariement) ;
• les méthodes mettant en oeuvre une SADCT ("Shape Adaptive DCT").

In particular, said method advantageously belongs to the group comprising:

• the methods implementing a CSD;
• methods based on fractal decomposition;
• the so-called "matching pursuit" methods (or matching pursuit methods);
• the methods implementing a SADCT ("Shape Adaptive DCT").

The method described above can of course be applied to an image (or a sequence of images) complete. It can also, according to one embodiment advantageous, to be implemented on image portions having a texture whose representation error is greater than a given threshold. Said error of representation may in particular correspond to a difference in luminance between said source triangle and the triangle after reconstruction.

In this case, the coding method is preferably implemented on an error image, corresponding to the difference between a source image and a approximate image, obtained by implementing a prior process separate from coding.

Said prior coding method may in particular be a method of approximation by refinement, implementing a hierarchical mesh with from which we build a quaternary tree with as many levels as there has levels in said hierarchical mesh, each of said levels presenting a number of nodes equal to the number of triangles in the mesh level corresponding. In this case, for the nodes meeting a predetermined criterion, advantageously, replacing said prior coding by a coding based on transformed as described above.

Said predetermined criterion can be based, according to one embodiment preferential, on the difference in luminance between the triangle of the approximate image and that of the source image.

• on calcule un écart de luminance entre l'image à coder et l'image interpolée sur ledit triangle, à partir des sommets du maillage emboíté auquel appartient le noeud considéré ;
• on compare ledit écart de luminance à un écart seuil ;
• on effectue le choix suivant :
  • si ledit écart de luminance est inférieur audit écart seuil, on interrompt le procédé d'approximation par raffinement du maillage hiérarchique, pour le noeud considéré ;
  • si ledit écart de luminance est supérieur audit écart seuil, mais inférieur à un second seuil, on continue à appliquer ledit procédé mettant en oeuvre un maillage hiérarchique ;
  • si ledit écart de luminance est supérieur audit second seuil, on met en oeuvre le procédé de codage décrit précédemment.

In this case, the processing for each node (knowing that a node corresponds to a triangle on a given level of the tree) is advantageously as follows:

• a luminance difference is calculated between the image to be coded and the image interpolated on said triangle, from the vertices of the nested mesh to which the considered node belongs;
• comparing said luminance difference to a threshold difference;
• the following choice is made:
  • if said luminance difference is less than said threshold difference, the method of approximation by refinement of the hierarchical mesh is interrupted for the node considered;
  • if said luminance difference is greater than said threshold difference, but less than a second threshold, said method continues to apply a hierarchical mesh;
  • if said luminance difference is greater than said second threshold, the coding method described above is implemented.

k : réel supérieur ou égal à 1 ;

S : valeur réelle proportionnelle à l'écart de luminance d'erreur moyen.

According to a particular embodiment of the invention, said second threshold is k × S, with:

k: real greater than or equal to 1;

S: actual value proportional to the mean error luminance deviation.

Preferably, said luminance difference represents an error quadratic or an absolute error between said source triangle and the triangle approximate corresponding.

a) application d'une transformation inverse à ladite seconde transformation réversible sur lesdites matrices transformées, délivrant lesdites matrices carrées reconstruites ;

b) association à chacune desdites matrices carrées reconstruites d'un triangle reconstruit correspondant, à l'aide d'une transformation affine inverse de ladite première transformation réversible ;

c) reconstruction de ladite partition minimale, à partir desdits triangles reconstruits.

The invention also relates to the decoders and the decoding of the coded images according to the coding method described above. The method for decoding data representative of a coded image according to the coding method of the invention notably comprises the following stages of reconstruction of an approximation of the original image:

a) applying an inverse transformation to said second reversible transformation on said transformed matrices, delivering said reconstructed square matrices;

b) association with each of said reconstructed square matrices of a corresponding reconstructed triangle, using an inverse affine transformation of said first reversible transformation;

c) reconstruction of said minimum partition, from said reconstructed triangles.

In other words, the reconstruction of the coded images is based, in particular, on the implementation of inverse transformations to those used during coding.

In particular, said square matrices can be recreated from data of a received bit stream, the decoded data of which are the coefficients of the triangle to be reconstructed, which form the lower part of said matrix.

When a pre-coding, as described above, has been implemented work, steps a), b) and c) are of course applied to the corresponding part of the received bitstream, the other part of the bitstream having been coded and being decoded by another method.

• un décodage préalable desdites données codées selon un codage préalable, permettant la description d'une représentation initiale ;
• un décodage complémentaire desdites données codées à l'aide desdites transformations réversibles, mettant en oeuvre lesdites étapes a), b) et c), et permettant d'affiner ladite représentation initiale.

Préférentiellement, ledit codage préalable mettant en oeuvre un codage hiérarchique, ledit décodage préalable assure la lecture, dans le train binaire reçu, d'au moins une des informations appartenant au groupe comprenant :

• le nombre de niveaux de la hiérarchie ;
• l'identification de la technique de codage utilisée pour chacun des triangles ;
• la succession des valeurs différentielles des composantes associées aux noeuds dudit maillage hiérarchique ;
• l'identification des arcs sur lesquels une inversion de diagonale est réalisée.

In particular, when the binary train comprises on the one hand data coded according to a prior coding, and on the other hand data coded using said reversible transformations, said decoding method comprises:

• a prior decoding of said coded data according to a prior coding, allowing the description of an initial representation;
• a complementary decoding of said coded data using said reversible transformations, implementing said steps a), b) and c), and making it possible to refine said initial representation.

Preferably, said prior coding implementing hierarchical coding, said prior decoding reads, in the received bit stream, at least one of the pieces of information belonging to the group comprising:

• the number of levels in the hierarchy;
• identification of the coding technique used for each of the triangles;
• the succession of differential values of the components associated with the nodes of said hierarchical mesh;
• the identification of the arcs on which a diagonal inversion is carried out.

• la figure 1, déjà commentée en préambule, illustre la technique connue d'un codage mettant en oeuvre une transformation ;
• la figure 2 est un organigramme simplifié du procédé de l'invention;
• la figure 3 illustre le principe des deuxième et troisième étapes du procédé de la figure 2 ;
• la figure 4 est un extrait, plus précis, de la figure 3, correspondant à la deuxième étape du procédé de la figure 1 ;
• les figures 5 et 6 présentent deux modes de quantification pouvant être utilisés dans le procédé de la figure 2 ;
• la figure 7 illustre le parcours en zig-zag de l'étape de codage du procédé de la figure 2 ;
• la figure 8 illustre la correspondance entre le maillage emboíté et l'arbre quaternaire dans un procédé de codage hiérarchique ;
• la figure 9 est un exemple de sélection des noeuds de l'arbre de la figure 8, sur lesquels le procédé de la figure 2 va être mis en oeuvre ;
• la figure 10 est un organigramme simplifié illustrant le choix du traitement à effectuer, lorsque l'on met en oeuvre de façon associée le procédé de l'invention et un codage hiérarchique.

Other characteristics and advantages of the invention will appear more clearly on reading the following description of a preferred embodiment given by way of simple illustrative and nonlimiting example, and of the appended drawings among which:

• FIG. 1, already commented on in the preamble, illustrates the known technique of coding implementing a transformation;
• Figure 2 is a simplified flowchart of the method of the invention;
• Figure 3 illustrates the principle of the second and third steps of the method of Figure 2;
• FIG. 4 is an extract, more precise, of FIG. 3, corresponding to the second step of the method of FIG. 1;
• Figures 5 and 6 show two quantification modes that can be used in the method of Figure 2;
• FIG. 7 illustrates the zigzag course of the coding step of the method of FIG. 2;
• FIG. 8 illustrates the correspondence between the nested mesh and the quaternary tree in a hierarchical coding method;
• Figure 9 is an example of selection of the nodes of the tree of Figure 8, on which the method of Figure 2 will be implemented;
• FIG. 10 is a simplified flowchart illustrating the choice of the processing to be carried out, when the method of the invention is implemented in association with a hierarchical coding.

The invention therefore proposes the implementation of a transformation, by example a DCT transformation, adapted to a triangular partition. Figure 2 is a general flowchart illustrating the corresponding process.

• définition 21, sur le domaine de l'image à coder, d'une partition triangulaire, qui peut être adaptée au contenu, sur le domaine de l'image (ou de la, ou des, portion(s) d'image) à coder ;
• détermination, pour chaque élément de la partition obtenue, des transformations permettant d'associer à chaque élément triangulaire un triangle de référence 22, puis un carré (c'est-à-dire une matrice) 23 ;
• réalisation d'une DCT 24 sur chacune de ces matrices ;
• application d'un procédé de quantification 25 et de codage 26, pouvant être identique à ceux des standards actuels.

The node processing according to the invention is therefore as follows:

• definition 21, on the domain of the image to be coded, of a triangular partition, which can be adapted to the content, on the domain of the image (or of the image portion (s)) to to code;
• determination, for each element of the partition obtained, of transformations making it possible to associate with each triangular element a reference triangle 22, then a square (that is to say a matrix) 23;
• creation of a CSD 24 on each of these matrices;
• application of a quantification 25 and coding method 26, which may be identical to those of current standards.

According to the first step 21 of the method of the invention, any first, on the image domain, a triangular partition. This partition triangular is usually initially regular (although it can also be irregular). It can therefore sometimes seem inappropriate, when it is regular, to represent an image with disparities in sound content and / or mixing uniform regions with more textured areas, requiring a high density of vertices.

This step 21 therefore advantageously comprises an optimization of the position of the vertices of the mesh defining the triangles, so as to move the concentrations of vertices of the mesh towards the zones requiring it. Such a technique is for example presented in patent document FR-98 12 525, at names of the owners of this patent application.

The most immediate visual effect of such optimization is manifested by a approximation of the vertices of the mesh to the physical contours of the object of the image.

The second and third steps 22 and 23 of the process of the invention are illustrated in Figure 3.

We determine, for each triangular element 31 of the partition, the affine transformation 32 allowing to associate with each arbitrary triangle 31 a reference triangle 33, which is isosceles. We then transform the triangle of reference in a square, and more precisely a square matrix 34, by symmetrization 35.

More specifically, the first transformation 32 consists in determining the affine transformation allowing to pass from any triangle 31 to the triangle 33, as illustrated in FIG. 4.

The reversible affine transformation F such that P ₁ = F (Q _i ), with P ₁ = (x ₁ , y ₁ ) and Q _i = (X ₁ , Y _i ), is written:

This affine transformation is invertible, because the determinant of the matrix is equal (except for the sign) to 2A (where A represents the area of any triangle 31), which is assumed to be non-zero. This inverse affine transformation is therefore written:

The second transformation 23, 36 consists in transposing the information contained in each triangle of area A in the lower part of a square matrix G of E (α × 2 × AT ) lines, where E represents the upper whole part of the value in parentheses, and α ∈ R ⁺ , * represents a scale factor, which acts on the visual representation of the image, by achieving an expansion (α> 1) or compression (α <1) in the spatial domain.

According to formulas (1) and (2), we have: F ( m, n ) = F ( n, m ) because I (x, y) = I (x, y), due to the symmetrization 35.

After symmetrization of G, its transformation 24 according to equation (1) also generates an equally symmetrical matrix H.

As a result, the information in the lower part of each matrix G being identical to the upper part (25), the use of the block based DCT 24 transformation can be implemented as for example in MPEG or JPEG.

After transformation 24, only the lower parts of the matrices H will be quantified (25) and coded (26).

• le facteur d'échelle α (on prendra alors α<1) ;
• le choix de la quantification, et en particulier amplitude des pas de quantification retenus

In order to optimize the performance of the coding cost 26, two means of action can be implemented, modulated for example as a function of the relevance of the texture underlying the triangles considered, namely:

• the scale factor α (we will then take α <1);
• the choice of quantification, and in particular the amplitude of the quantification steps selected

• une quantification uniforme ;
• une quantification à parcours zig-zag ;
• une quantification par utilisation d'une matrice de pondération pré-évaluée sur critère psycho-visuel.

Among the possible quantifications, it is possible in particular to use:

• uniform quantification;
• a zig-zag quantization;
• quantification by using a pre-evaluated weighting matrix based on psycho-visual criteria.

Quantification with a zig-zag course consists in initializing the quantification process to a value Q ⁰ _AC , which during the course, at each ascent, is incremented by a value Δ _AC , as illustrated by the arrow 51 of Figure 5.

An example of a pre-evaluated weighting matrix based on psycho-visual criteria is the QM standard JPEG matrix. illustrated in figure 6. We can also consider the matrix of the MPEG4 standard. The matrices G and QM can be of different size, we will interpolate the QM matrix, bringing the latter at the size of G as for JPEG, it is then possible to define a quality factor qf acting as a multiplier to the QM matrix. We can also implement an optimized weighting matrix for the image treated

The effective coding 26 is for example carried out by performing a coding of RLE (Run Length Encoding) and entropy type, on the zig-zag route 71 shown in figure 7.

It is clear that the method described above can be used alone, on full images.

It can also, advantageously, be implemented on portions images, in addition to another coding approach. In particular, it can advantageously be used selectively on particular regions of the image, especially the highly textured parts.

Thus, for example, the method of the invention proves to be particularly well adapted to the coding technique described in patent application FR-98 12 525, in the name of the same owners as this patent application, and having as title "coding process for still or moving images with reduction and adaptation of the flow ". It appears that this latter technique has difficulties in represent textures.

Before showing how the process of the invention can be used in this way, the principle of the process described in the patent application is briefly recalled FR-98 12 525.

• définir, sur un domaine de l'image à coder, un maillage hiérarchique comportant une pluralité de maillages emboítés dont les sommets de mailles peuvent être des pixels de ladite image ;
• réaliser les optimisations de luminance, chrominance, et positions sur chaque niveau de maillage ;
• déterminer, pour chaque maille dudit maillage hiérarchique, un écart de luminance entre l'image à coder et une image interpolée obtenue à partir des sommets du maillage emboíté auquel appartient la maille considérée, et
• introduire dans le train binaire les valeurs (avantageusement codées en différentiel par rapport au niveau hiérarchique précédent) de positions, de luminance et de chrominance des sommets des mailles dont l'écart de luminance est supérieur à un écart seuil.

The object of this technique is a method of coding a digital image, aimed at producing a bit stream representative of this image, the length of the bit stream being a function of the desired representation. This process involves the following steps:

• define, on a domain of the image to be coded, a hierarchical mesh comprising a plurality of nested meshes whose mesh vertices may be pixels of said image;
• perform optimizations of luminance, chrominance, and positions on each level of mesh;
• determining, for each mesh of said hierarchical mesh, a luminance difference between the image to be coded and an interpolated image obtained from the vertices of the nested mesh to which the mesh considered belongs, and
• introduce into the binary train the values (advantageously coded in differential with respect to the previous hierarchical level) of positions, luminance and chrominance of the vertices of the meshes whose luminance difference is greater than a threshold difference.

Note that this technique is not limited to luminance signals and chroma, but can be applied to any color scheme.

The process of the present invention can advantageously take place during of the calculation of this threshold deviation.

Indeed, according to the prior art, and as illustrated by the figure 8, at the end of the mesh stage, we build a tree structure quaternary 81, associated with hierarchical mesh 82, to manipulate values (colors and positions) of the vertices of the meshes. Tree 81 has a number of nodes equal to the number of triangles in the corresponding mesh level. Each node 83 of the tree relates to a single triangle 84 of the mesh hierarchical 82.

Once the tree 81 has been constructed, it is necessary to determine the data of the tree to introduce into the bit stream representative of the image. This determination depends on the desired quality.

To make this determination, we plan to calculate, for each triangle, a difference in luminance between the image to be coded and the image interpolated from vertices of the nested mesh to which the mesh in question belongs. This gap is then compared to a threshold deviation for each triangle. The value of the threshold deviation is a function of the desired quality of representation.

We then introduce the part of the tree relating to the binary train triangles with a greater luminance difference. This selection of nodes the tree by deep path is illustrated in figure 9. Only are kept the knots over the border 91.

The threshold difference therefore makes it possible to transmit the data relating to the image depending on the local quality of these different triangular partitions. Indeed, on a textured part, data transmission occurs up to the last level of mesh (finest mesh) and, for smoother parts, a coarse level is sufficient.

According to the present invention, it is advantageously possible to mix the two approaches, namely affine, symmetrized and transformed transmission by DCT (named for the sake of brevity DCT thereafter), with the technique of nested meshes which has just been described.

Indeed, according to this technique of nested meshes, we define everything first, on the domain of the image to be coded, a hierarchical mesh comprising a plurality of nested meshes. The vertices of these meshes are pixels of the image to be coded. This mesh is for example obtained by regular divisions and successive meshes of the coarse mesh.

According to the present invention, one places oneself at a level n (between the first and last level of mesh) of mesh, we compute the image interpolated by the hierarchical mesh technique, and we deduce an image error corresponding to the difference in luminance between the original image and the interpolated image.

The tree relating to the first n levels of meshes is then constructed, and the luminance difference is calculated for each of the triangles of the mesh of the error image, and a threshold difference S is chosen. The criterion of the difference of luminance on a triangle T corresponds to the following quadratic error:

With I, the error image between the interpolated image and the original image on the triangle T.

• 101 : inférieur à l'écart seuil : la partie de l'image interpolée sur ce triangle est d'une qualité visuelle correcte, et la procédure s'arrête (102) ;
• 103 : supérieur à l'écart seuil mais inférieur à k x S, avec k ≥ 1 : le procédé d'approximation continu avec la technique du maillage hiérarchique (104), la partie de l'image interpolée correspondant à une image moyennement texturée ;
• 105 : supérieur à k x S avec k ≥ 1 : le triangle est traité par une DCT appliquée au triangle de l'image d'erreur (106).

According to the present invention, the nodes of the tree are then determined making it possible to specify whether the approximation procedure should stop, whether the subdivision of the mesh should be continued by affine interpolation with the hierarchical mesh technique, or whether the DCT must be used according to the technique described above. For that, one can use the method illustrated in figure 10. If, for the level n given, the difference in luminance of a triangle T of the mesh is:

• 101: less than the threshold deviation: the part of the image interpolated on this triangle is of correct visual quality, and the procedure stops (102);
• 103: greater than the threshold deviation but less than kx S, with k ≥ 1: the continuous approximation method with the hierarchical mesh technique (104), the part of the interpolated image corresponding to a moderately textured image;
• 105: greater than kx S with k ≥ 1: the triangle is processed by a DCT applied to the triangle of the error image (106).

d'où:

donc :

This selection is justified in the following manner. We know that :

from where:

therefore :

We therefore observe that the coefficient F (m, n) tends to zero when the difference of luminance tends to zero. A small quadratic error results in AC coefficients after transform of low amplitude, with high chances to be canceled after quantification.

Thus, performing on such meshes a less costly affine interpolation that a DCT transformation is more judicious.

The overall process therefore consists in processing part of the image by the hierarchical mesh technique, and to treat the highly textured parts of this image by a DCT according to the present invention, applied to triangles of the corresponding error image.

We therefore apply here on the textured part of the error image a DCT on triangles with a large luminance difference.

• les méthodes à base de décomposition fractale : le principe de compression d'images en niveaux de gris par la méthode des IFS, aussi appelée compression fractale, repose sur l'expression du contenu de l'image au moyen du contenu lui-même.
  Il peut être vu comme une auto-quantification de l'image. La formalisation de cette méthode provient notamment des travaux de Hutchinson en 1981, et de ceux de Bradley, Demko et d'autres chercheurs du Georgia Institute of Technology entre 1985 et 1988. Le premier algorithme automatique appliquant ces idées à la compression des images a été proposé par Jacquin en 1989.
  Des améliorations à cette technique sont proposées dans le document de brevet FR- 99 00656, intitulé "procédé et dispositif de codage a base de schémas IFS, à fonctions de collage oscillantes, procédé de codage, fonction de collage, support de données et applications correspondants".
• les methodes dites de "matching pursuit" (encore appelées poursuites d'appariemments), notamment décrit dans l'article de Ralph Neff et Avideh Zakhor, intitulé "Very Low Bit Rate Video Coding based on Matching Pursuits", publié dans IEEE Transactions on circuits and systems for video technology.
  Le codage (du résidu) par matching pursuit est une méthode itérative qui utilise un dictionnaire de fonctions redondantes. A chaque itération, on cherche la fonction qui représente le mieux le résidu obtenu à l'étape précédente. On décompose ainsi l'image sur une suite d'atomes qui la représentent de manière optimale ;
• la SADCT ("Shape Adaptive DCT"), décrite par exemple par T. Sikora et B. Makai dans "Shape Adaptive DCT for generic Coding" (IEEE Transactions on Circuits and Systems for Video Technology, 5(1), pp. 59 - 62, février 1995).

In addition, the hierarchical mesh technique is just one example. The technique of the invention implementing a DCT on triangles can be used by any other technique using triangles, such as for example:

• methods based on fractal decomposition: the principle of compression of grayscale images by the IFS method, also called fractal compression, is based on the expression of the content of the image by means of the content itself.
  It can be seen as an auto-quantification of the image. The formalization of this method comes in particular from the work of Hutchinson in 1981, and that of Bradley, Demko and other researchers from the Georgia Institute of Technology between 1985 and 1988. The first automatic algorithm applying these ideas to image compression was proposed by Jacquin in 1989.
  Improvements to this technique are proposed in patent document FR-99 00656, entitled "coding method and device based on IFS schemes, with oscillating bonding functions, coding method, bonding function, data carrier and corresponding applications ".
• the so-called "matching pursuit" methods (also called matching pursuits), notably described in the article by Ralph Neff and Avideh Zakhor, entitled "Very Low Bit Rate Video Coding based on Matching Pursuits", published in IEEE Transactions on circuits and systems for video technology.
  The coding (of the residue) by matching pursuit is an iterative method which uses a dictionary of redundant functions. At each iteration, we look for the function that best represents the residue obtained in the previous step. We thus decompose the image on a series of atoms which represent it optimally;
• SADCT ("Shape Adaptive DCT"), described for example by T. Sikora and B. Makai in "Shape Adaptive DCT for generic Coding" (IEEE Transactions on Circuits and Systems for Video Technology, 5 (1), pp. 59 - 62, February 1995).

The invention also relates to the decoding of the data coded according to the coding method described above. This decoding process is deduced directly from the coding steps.

• la description d'une représentation initiale de l'image, issue du codage préalable (qui sera soumise à un décodage préalable symétrique) ;
• les valeurs quantifiées et codées après transformation DCT associées aux triangles sélectionnés.

Thus, when a prior coding, in particular of hierarchical type has been implemented, the decoding is based on the reception of a bit stream containing:

• the description of an initial representation of the image, resulting from the prior coding (which will be subject to a symmetrical prior decoding);
• the quantified and coded values after DCT transformation associated with the selected triangles.

The weighting coefficients of the matrices can be transmitted in the binary train. However, preferably, they are known to the decoder.

• création d'une matrice carrée symétrique dont la partie inférieure comprend les coefficients décodés du triangle à représenter, lu dans le train binaire ;
• transformation DCT inverse de la matrice ainsi créée ;
• transformation affine du triangle rectangle isocèle associé à la partie inférieure de la matrice, vers le triangle à représenter.

Lorsque le codage préalable repose sur un maillage hiérarchique, le décodage correspondant assure notamment la lecture, dans le train binaire reçu :

• du nombre de niveaux de la hiérarchie ;
• de l'identification de la technique de codage utilisée pour chacun des triangles ;
• de la succession des valeurs différentielles des composantes associées aux noeuds dudit maillage hiérarchique.

The decoding of the quantized and coded values after DCT transformation notably comprises the following steps:

• creation of a symmetrical square matrix, the lower part of which includes the decoded coefficients of the triangle to be represented, read in the binary train;
• inverse DCT transformation of the matrix thus created;
• affine transformation of the isosceles right triangle associated with the lower part of the matrix, towards the triangle to represent.

When the prior coding is based on a hierarchical mesh, the corresponding decoding ensures in particular the reading, in the bit stream received:

• the number of levels in the hierarchy;
• identification of the coding technique used for each of the triangles;
• of the succession of the differential values of the components associated with the nodes of said hierarchical mesh.

Claims (24)

1. Method for image coding, characterised in that it comprises, for a domain corresponding to at least one image portion, the following steps:

   defining (21) a minimum triangular partition covering the said domain;

   associating with each of the said source triangles a square matrix (34) representing the said source triangle (31), with the aid of a reversible first transformation (22, 23);

   applying (24) a reversible decorrelating second transformation to each of the said square matrices, delivering transformed matrices.
2. Method for image coding according to Claim 1, characterised in that the said step of associating a square matrix comprises the following steps:

   affine transformation (32) of a source triangle (31) into a right-angled isosceles triangle (33), referred to as the reference triangle;

   creation (36) of a square matrix (34) whose lower part comprises the data representing the said right-angled isosceles triangle (33);

   symmetrisation (35) of the said square matrix.
3. Method for image coding according to Claim 2, characterised in that the step (36) of creating a square matrix implements a scale factor α permitting expansion or compression in the space domain.
4. Method for image coding according to Claim 3,
   characterised in that the said square matrix comprises E(α × 2 × A) rows, where E represents the upper integer part, A being the area of the said right-angled isosceles triangle.
5. Method for image coding according to any one of Claims 1 to 4, characterised in that the said second transformation belongs to the group comprising:

   the Karhunen Loève transform (KLT);

   the discrete Fourier transform (DFT) ;

   the discrete cosine transform (DCT) ;

   the Walsh-Hadamard transform (WHT).
6. Method for image coding according to any one of Claims 1 to 5, characterised in that it comprises a step of quantising (25) and coding (26) the data of the lower part of the said transformed matrix.
7. Method for image coding according to Claim 6, characterised in that the said quantisation (25) belongs to the group comprising:

   uniform quantisation;

   zigzag-path quantisation, the quantisation step size being incremented as the path proceeds;

   quantisation based on at least one weighting matrix which is pre-evaluated or optimised for the image being processed.
8. Method for image coding according to any one of Claims 4 to 7, characterised in that the said scale factor α, the quantisation type and/or the quantisation step size can be modified for each of the said triangles and/or for each of the said image portions.
9. Method for image coding according to any one of Claims 6 to 8, characterised in that it comprises a step of RLE and entropic coding (26) of the quantised data.
10. Method for image coding according to any one of Claims 1 to 9, characterised in that the said triangular partition is obtained according to a method which takes into account the content of the image or of the image portion.
11. Method for image coding according to Claim 10, characterised in that the said method belongs to the group comprising:

    methods based on fractal decomposition;

    so-called "matching-pursuit" methods;

    methods implementing an SADCT;

    methods implementing a DCT.
12. Method for image coding according to any one of Claims 1 to 11, characterised in that it is implemented (106) on image portions having a texture whose representation error is greater than a given threshold (103).
13. Method for image coding according to any one of Claims 1 to 12, characterised in that the said representation error corresponds to a deviation in luminance between the said source triangle and the triangle after reconstruction.
14. Method for image coding according to any one of Claims 1 to 13, characterised in that it is implemented on an error image, corresponding to the difference between a source image and an approximated image, which is obtained by implementing a separate prior coding method.
15. Method for image coding according to Claim 14, characterised in that the said prior coding method is a method of approximation by refinement implementing a hierarchical mesh, based on which a quaternary tree is constructed having as many levels as there are levels in the said hierarchical mesh, each of the said levels having a number of nodes equal to the number of triangles in the corresponding mesh level,
    and in that, for the nodes satisfying a predetermined criterion (103), the said prior coding is replaced by coding according to any one of Claims 1 to 11.
16. Method for image coding according to Claim 15, characterised in that the said predetermined criterion is based on the deviation in luminance between the triangle of the approximated image and that of the source image.
17. Method for image coding according to Claim 16, characterised in that, for each node:

    a deviation in luminance is calculated between the image to be coded and the interpolated image based on the vertices of the nested mesh to which the node in question belongs;

    the said luminance deviation is compared with a threshold deviation;

    the following choice is made:

    if the said luminance deviation is less than the said threshold deviation, the method of approximation by refining the hierarchical mesh is stopped for the node in question;

    if the said luminance deviation is greater than the said threshold deviation, but less than a second threshold, the said method implementing (106) a hierarchical mesh continues (104) to be applied;

    if the said luminance deviation is greater than the said second threshold, the coding method according to any one of Claims 1 to 11 is implemented.
18. Method for image coding according to Claim 17, characterised in that the said second threshold is equal to k×S, with:

    k: real number greater than or equal to 1;

    S: real value proportional to the mean-error luminance deviation.
19. Method for image coding according to any one of Claims 16 to 18, characterised in that the said luminance deviation represents a quadratic error or an absolute error between the said source triangle and the corresponding approximated triangle.
20. Method for decoding data representing an image coded according to a method comprising, for a domain corresponding to at least one image portion, the following steps:

    defining a minimum triangular partition covering the said domain;

    associating with each of the said source triangles a square matrix representing the said source triangle, with the aid of a reversible first transformation;

    applying a reversible decorrelating second transformation to each of the said square matrices, delivering transformed matrices,

    characterised in that it comprises the following steps of reconstructing an approximation of the original image:

    a) applying a transform which is the inverse of the said reversible decorrelating second transformation to the said transformed matrices, delivering the said reconstructed square matrices;

    b) associating with each of the said reconstructed square matrices a corresponding reconstructed triangle, with the aid of an affine transformation which is the inverse of the said reversible first transformation;

    c) reconstructing the said minimum partition, based on the said reconstructed triangles.
21. Decoding method according to Claim 20, characterised in that the said square matrices are recreated based on the data of a received bit stream, whose decoded data are the coefficients of the triangle to be reconstructed, which form the lower part of the said matrix.
22. Decoding method according to either one of Claims 20 and 21, characterised in that steps a), b) and c) are implemented on only a part of the received bit stream, the other part of the bit stream having been coded, and being decoded, according to another method.
23. Decoding method according to Claim 22, characterised in that the said bit stream comprises, on the one hand, data coded according to prior coding and, on the other hand, data coded with the aid of the said reversible transformations, the said decoding method comprising:

    prior decoding of the said data which were coded according to prior coding, making it possible to describe an initial representation;

    complementary decoding of the said data which were coded with the aid of the said reversible transformations, implementing the said steps a), b) and c), making it possible to refine the said initial representation.
24. Decoding method according to either one of Claims 22 and 23, characterised in that, with the said prior coding implementing hierarchical coding, the said prior decoding reads, from the received bit stream, at least one of the information items belonging to the group comprising:

    the number of levels in the hierarchy;

    identification of the coding technique used for each of the triangles;

    the sequence of differential values of the components associated with the nodes of the said hierarchical mesh;

    identification of the arcs on which diagonal inversion is carried out.

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